Arabesque, Pirouette, Cha-cha-cha

As with a dance, problems become much more interesting when they are composed of several different kinds of steps.

Do your students struggle with multi-step word problems? Encourage students to think of each problem as a story, and have them tell the story, without any numbers, verbally or in writing, in their own words. Then have students model the story with a Singapore Model Method drawing or other picture, table, diagram, or chart that helps them to organize the information they know.

When solving the problem, remind students to pay careful attention to labeling what each number represents, and to include units along with numbers in order to follow the actions and relationships in the story.

Remember to always begin with a full sentence that answers the question, leaving a blank for the solution.

Here are some problems to get you started:

1) Ms. Delmore is planning her summer vacation to Australia to visit the famous Sydney Opera House. She can pay for the vacation with a deposit of $1,395 and 9 additional monthly payments of $485 each. She can also make a one-time payment of $5,495. Which option will cost more? How much more? Why do you think the two options are offered? Why is one more expensive than the other? Which would you choose if you were Ms. Delmore?

2) Linda and Hazel are selling Girl Scout cookies. Linda’s parents buy three times as many cookies as Hazel’s parents. Since she has so many cookies, Linda decides to share some with her friends. After Linda shared 50 cookies, she had only half as many cookies as Hazel. How many cookies did Hazel have?

3) Each month, Mr. Marshal spends $40,000 to pay the salespeople and janitors in his store. The 46 salespeople each receive $820. How much is each of the four janitors paid?

4) The produce manager at the supermarket received a shipment of 27 cartons of apples. Each carton contained 65 apples. On Monday he sold 184 apples and on Tuesday he sold 218 apples. He then sold an equal number of apples each day for the remainder of the week. If he had to throw away the last 13 apples because they were rotten, how many apples did he sell over the weekend?

5) A man won $100,000 in the lottery! He spent $8,000 on some new furniture for his home, and decided to divide the rest into 8 equal portions. He gave 4 portions to his wife, one portion to his son, and shared the remaining portions equally among five of his favorite charities. How much more money did his son get than each charity?

6) Charlie is in charge of purchasing for mens’ clothing for the department store in the mall. Noticing a particularly popular style of belt, he decided to buy 17 dozen. The store sold 196 of the belts at $9 each, and then decided to change the price due to their popularity. If the total amount collected from the sale of all the belts was $1,860, what was the difference in price from the original price to the new price? Was it an increase or a decrease? By what percent did the price change?

7) Charlie next purchased fourteen boxes of tee shirts for his store at $120 per box. Each box had two dozen shirts. The store sold 149 of the shirts during a grand sale at $8 each, and then the rest at $12 each. Charlie will receive a bonus of $25 every time the store makes a profit of $500 on an item he purchased. Will Charlie receive a bonus for his tee shirt purchase? If so, how much will he receive?

8) A farmer raised ducks and chickens. In January, he had twice as many ducks as chickens. In February, 19 ducks squeezed through a hole in the fence and ran away. In March, the farmer sold 413 ducks, and then had only half as many ducks as chickens. How many chickens did the farmer have?

9) The Mathletes are trying to raise $100 to rent a bus that will take them to a math competition. They notice that teachers at their school are always losing their pens, and decide to buy some pens and sell them to the teachers with the profits going toward the bus rental. They buy a dozen boxes, each with 48 pens, at $13 per box. They then repack 7 of those boxes into packages of 12 pens each and sell them for $5 per box. They decide to sell the remaining pens at 4 for $2. Will they make enough money to cover the bus rental fee?

10) Jack proposed to Jill on the hill and now they are getting married! They hire a tailor to make dresses and suits for their large bridal party. The tailor takes twice as much time to make 3 dresses as he would need to make 5 suits. It takes him 90 hours altogether to make 9 dresses and 15 suits, but he needs to make two more suits for two last minute additions to the bridal party. He decides to hire another tailor who works at the same rate and pay him $25 per hour to make the two suits. How much will he need to pay the tailor?